Hello,
I am in Calgary Canada right now, and am currently researching destinations to set my TESOL certified butt down!
I really would like to work in Europe (Spain, Germany, Italy). I have my TESOL, a BA and some teaching experiance.
Anywho...
Would it be impossible to get a job without a EU passport? Could I get citizenship if my granddad is from the UK? So, in general I am clueless about work permits and job opportunities in Europe...
Could someone help?

No you can't get a British passport on the strength of a British grandparent. To get a British passport automatically you must have one parent who was a British citizen (by birth - ie born in the UK) and your parents must have been married when you were born.

As for getting a job in the EU without an EU passport: it will be possible but varies from country to country. Some countries are much easier (for example Poland plans to remove the need for work permits for ALL native speaker language teachers) some are harder (Holland is supposed to be all but impossible for non-EU citizens). It also depends what kind of job you want. If you are happy working illegally then there is work in Spain and Italy. But working illegally opens you up to all sorts of risks....

...To get a British passport automatically you must have one parent who was a British citizen (by birth - ie born in the UK) and your parents must have been married when you were born.

If that is true then I have the best passport forgery in the world. Neither of my parents were born as UK citizens (or subjects for that matter).

My father got his on the basis of the British army having already recruited him and promoted him before anyone bothered asking what nationality he was. I then got mine of the basis of my father having the right nationality when I was born and my parents being married.

Unfortunately, I don't think this loophole is that easy to use, as you'd have to ask your father to travel back in time, join the British army, and successfully avoid anyone asking about his nationality. This is a non-trivial task.